Soft octopus-inspired suction cups using dielectric elastomer actuators with sensing capabilities

Bioinspired and biomimetic soft grippers are rapidly growing fields. They represent an advancement in soft robotics as they emulate the adaptability and flexibility of biological end effectors. A prominent example of a gripping mechanism found in nature is the octopus tentacle, enabling the animal to attach to rough and irregular surfaces. Inspired by the structure and morphology of the tentacles, this study introduces a novel design, fabrication, and characterization method of dielectric elastomer suction cups. To grasp objects, the developed suction cups perform out-of-plane deflections as the suction mechanism. Their attachment mechanism resembles that of their biological counterparts, as they do not require a pre-stretch over a rigid frame or any external hydraulic or pneumatic support to form and hold the dome structure of the suction cups. The realized artificial suction cups demonstrate the capability of generating a negative pressure up to 1.3 kPa in air and grasping and lifting objects with a maximum 58 g weight under an actuation voltage of 6 kV. They also have sensing capabilities to determine whether the grasping was successful without the need of lifting the objects.


Introduction
Bioinspired and biomimetic soft robotics are significantly changing the field of robotics research.Researchers are studying how various mechanisms have evolved in nature, aiming to mimic the adaptability and versatility of biological systems without necessarily replicating their exact structure [1][2][3][4].Such robots aim to impersonate a variety of functions from the animal and plant kingdom, including the suction capabilities of octopus suction cups [5][6][7], the adhesive properties of gecko feet [8], the movement of octopus tentacles [9][10][11], the grasping mechanism found in bird claws [12], the walking gait of insects [13], or the snapping mechanism of the Venus flytrap [14,15].
Bioinspired soft grippers are an innovative branch of soft robotics.They are often made of flexible and compliant materials, such as polymers and hydrogels, which can deform and conform to the shape of the object they are grasping in response to external stimuli, such as temperature, voltage, light, or pH [16,17].For example, a bloodworm-inspired soft gripper has been developed for adaptable grasping [18].Another example is a soft gripper inspired by the scales of a pangolin, which can change its stiffness to adapt to different objects [19].The advantage of bioinspired soft grippers (compared to traditional rigid grippers) lies in their ability to handle delicate and irregularly shaped objects [20].This makes them invaluable in applications like smart actuators, flexible electronics, robotic surgery, health care, and prosthetics-where precision and adaptability are essential [17,21,22].
Within the field of bioinspired soft grippers, the unique morphology and gripping mechanism of octopus suction cups have inspired the development of versatile artificial suction cups [23].These grippers are designed to mimic the unique features of octopus tentacles, enabling the artificial counterpart to bend, wrap around objects, and form strong seals with their (a) a drawing of the morphology of an octopus suction cup where A is the acetabulum, I is the infundibulum, and C, R, and M represent the circular, radial, and meridional muscles, respectively [28], and (b) surface and volume increase of acetabulum due to contraction of radial muscles which results in a pressure drop of the enclosed fluid.Adapted with permission from [28].
suction cups.Such a mechanism can securely hold objects of different shapes, sizes, and textures [24,25].
Designing and fabricating such grippers requires first a deep understanding of the morphology of octopus tentacles.Octopus suction cups (also known as 'octopus suckers' or simply 'suckers') are composed of two main parts: the infundibulum, which is the externally visible disc-like portion that comes into contact with the object, and the acetabulum, which is the central cavity that is responsible for creating suction on objects [26].Suckers consist of a tightly packed three-dimensional array of musculature, including radial, circular, and meridional muscles, as shown in figure 1 [27].They are attached to the tentacle by a muscular base that can rotate the cup in any direction and elongate it to twice its normal length [28].
When a suction cup comes into contact with an object, it flattens and conforms to the surface to create a seal.The radial muscles thin the acetabulum wall, thereby increasing the enclosed volume.If the sucker is sealed to a surface, the cohesiveness of water resists this expansion; thus, the pressure of the enclosed water decreases instead.The pressure decrease also happens when the sucker is filled with a compressible fluid like air [29].To detach, the meridional and circular muscles antagonize the radial muscles [28].
A lot of thorough research has been done to develop octopus-inspired suction cups [30][31][32][33][34][35].For instance, Wu et al developed a soft gripper for underwater self-adaptive grasping and sensing-inspired by the glowing sucker octopus [36].Tramacere et al investigated the contribution of surface morphology in artificial suction cups during wet attachment conditions [37].Shahabi et al developed suction cups with four embedded strain sensors made up of microfluidic channels that allow the sucker to sense contact with objects [38].Zhang et al developed hydraulically coupled dielectric elastomer actuators (DEAs) based on the properties of hydraulically amplified selfhealing electrostatic actuators [39].Another noteworthy study was conducted by Sholl et al, in which they designed and fabricated a fully soft artificial suction cup inspired by cephalopods and decapods made of DEAs using carbon grease electrodes and acrylic elastomer VHB ™ tapes.They produced negative pressures in electroactive cylindrical vessels that expand radially and longitudinally [40].Capri et al presented buckling DEAs by placing the planar actuator on a substrate with a support to give an initial out-of-plane deflection to the actuator and constraining it with a ring [41].Last but not least, we mention the distinguished study on hydrostatically coupled octopusinspired DE suction cups, carried out by Follador et al, in which they designed, modeled, and fabricated a suction cup composed of a passive infundibulum and a DEA infundibulum [42].
Among the various actuation technologies (such as pneumatic, cable-driven, hydraulic, magnetic, shape memory alloy, electro-adhesive, and electroactive polymers [43]) DEAs are one of the most suitable options for mimicking the function of radial muscles.That is because they have been extensively studied and have an outstanding actuation technique, making them widely used in bionic robotics [44].Although pneumatic actuation is the most popular method for enabling soft robots to grip various objects, it requires an external source of compressed air.This dependency not only consumes more energy than DEAs [43] but also limits the mobility and autonomy of the robot.DEAs require a rather low actuation energy, which allows DEAs to be potentially integrated into the driving and measuring circuit units so they function autonomously.Ultimately in some applications, the actuation energy could be harvested from sustainable sources, such as ultra-high voltage solar modules [45,46] resulting in energyautonomous soft grippers.
DEAs are composed of soft and flexible elastomer layers, sandwiched between two compliant electrode layers.When the two electrodes are connected to a voltage source, opposite charges accumulate on the electrode layers.The electrostatic forces between the opposite charges attract each other, consequently compressing the elastomer layer.However, while the thickness is compressed, the area is expanded (figure 2)-due to the incompressibility of the elastomers.This type of actuation is similar to how radial muscles contract in an octopus suction cup, thus producing a negative pressure.There are, however, challenges when it comes to designing and fabricating dielectric elastomer suction cups.First of all, DEAs are, in general, planar actuators, meaning they perform an in-plane expansion.They also often need to be pre-stretched over a 2D rigid frame to stay in place.Fabricating DEAs in 3D shapes is therefore challenging because conventional deposition techniques mostly take place inplane (e.g. with spin-coating uncured elastomer compounds, pre-stretching elastomer tapes, and implementing electrode layers); therefore, we need to find a way to translate the planar actuation of DEAs to the out-of-plane actuation of a suction cups.Embedding rigid backbones enables DEAs to actuate out-of-plane [47,48].In this work, we employed an improved version of this technique and embedded soft backbones to produce fully soft suction cups made of dielectric elastomers (DE suction cups) that do not require a pre-stretch over a rigid frame or, in general, any external support.We elaborate on the design and fabrication methods for producing such dielectric elastomer suction cups in this article.
The second challenge that needs to be addressed before trying to lift an object concerns the seal; we must detect if the DE suction cup successfully sealed to the object's surface.As previously noted, a seal must be formed in order for the gripping mechanism to work.The most straightforward way to detect if the seal had been successful would be to measure the pressure of the fluid enclosed within the suction cup.However, this method would require an embedded pressure sensor in the suction cup, which makes the fabrication process unnecessarily complex.
Rather, we employed a sensorless detection or estimation method, which extracts information from the intrinsic properties of dielectric elastomers [49,50].In this research, we elucidate how to detect the seal formation simply by measuring the electrical capacitance of the DE suction cups without using a pressure sensor.We present an analytical capacitance model and an experimental approach for measuring the capacitance of the DE suction cups.This feature enables the DE suction cups to sense if the seal was successful before lifting any objects.
As a next step, we present a setup we developed to conduct studies on the suction pressure of the actuators.We finally demonstrate the DE suction cups grasping and lifting objects.

Design and fabrication
Building suction cups first requires selecting appropriate materials, and the literature recommends several readily available, elastomers [51].Two of the most popular ones are acrylic and silicone elastomers.Among the acrylic elastomers, VHB ™ tape (from 3M ™ ) has shown promising actuation behavior [52,53].However, they generally need to be pre-stretched over a rigid frame in order to unleash their maximum actuation potential.On top of that, VHB ™ tapes have viscoelastic behavior, making them suboptimal for dynamic actuation due to the dampening properties of viscoelastic materials.On the contrary, silicone elastomers are less viscoelastic, which is better for dynamic actuation.However, under the same amount of voltage, silicone elastomers deflect less than acrylic elastomers [54,55].In this work, we used Ecoflex ™ 00-10 silicone rubber (Smooth-on Inc., Macungie, PA, USA) as the elastomer, which is the softest silicone rubber available within the Ecoflex ™ series.We added Silicone Thinner ™ (Smooth-on Inc., Macungie, PA, USA) to the uncured silicone compound to make the elastomer even softer (elastic modulus of 27 ± 2 kPa).We used spin-coating to deposit thin and even elastomer layers in a typical thickness of 50 µm (for passive layers) and 550 µm (for active layers) and cured them in an oven (UF110, Memmert) for 15 min at 80 • C. Afterward, we painted carbon black (CB) powder (P250, Ensaco) directly onto the elastomer layer to pattern electrode layers.The CB particles adhere very well to the silicone rubber and result in an even pattern with clean edges.We achieved multi-layer actuators by repeatedly depositing elastomer and electrode layers in alternate succession.The fabrication process is illustrated in figure 3.
To transform a flat DEA into a curved acetabulum, we first 3D-printed a negative mold in the shape of a disc.The disc had a paraboloid cavity with an opening diameter of 20 mm and a depth of 10 mm.After fabricating the flat, planar DEA, we placed the actuator onto the mold so that the center of the actuator rested in the negative mold and took the paraboloid form.In this procedure, we needed to minimize the built-up mechanical stress inside the actuator, so we slid the actuator inside the paraboloid cavity instead of stretching it.Then, we placed the mold with the actuator as a substrate onto the spin-coating machine.While the machine was spinning, we used a  syringe to apply an uncured layer of Smooth-Sil ™ 950 (Smooth-on Inc., Macungie, PA, USA) at the edge of the paraboloid.By depositing Smooth-Sil ™ 950 (as a backbone material) off-center, we created a smooth, thin layer with a circular hole in the middle, which became the opening of the suction cup.Eventually, after curing the final layer, we took the actuator out of the mold and flipped it, as depicted in figures 4 and 5.
After removing the actuator from the mold, we observed that the dome height decreased from 10 mm (the dimension of the cavity) to less than 4 mm.In this paper, we refer to this phenomenon as 'dome recession' .
When the flat and planar actuator is placed onto the mold, it undergoes a certain degree of mechanical stress to adapt to the geometry of the paraboloid cavity.Depositing the backbone off-center introduces a stress-free layer around the opening of the dome.
When the actuator is released and no longer constrained by the mold, the mechanical stress, stored in the suction cup, attempts to return to its flat, stressfree state.This attempt, however, is counteracted by the backbone layer, as flattening the actuator exerts a mechanical stress on the backbone layer.As a result, the dome height decreases until the point where the dome structure and the backbone layer reach a mechanical equilibrium state.
Smooth-Sil ™ 950 is a soft silicone rubber with an elastic modulus of 1.9 MPa [56], which is approximately 32 times higher than Ecoflex ™ 00-10 [57]; therefore, it holds and supports the dome structure after the suction cup is removed from the mold.Nevertheless, when compared to the Ecoflex ™ series, the surface of Smooth-Sil ™ 950 is slippery, thus it is not a suitable finishing material for a gripper.On that account, we applied a final layer of Ecoflex ™ 00-30 on

Detecting the seal formation
As mentioned before, the foremost crucial step of a suction-based gripping mechanism is forming a proper seal between the suction cup and the object's surface.Without a proper seal, the fluid pressure inside the cup does not decrease, hence, the DE suction cup fails to grasp objects.When handling more delicate objects, it is especially important to make sure that gripping is successful before the object is lifted.In this section, we present a method to detect if a seal has been formed.For that, we take a closer look into the capacitance change of the suction cups during actuation and gripping.
In principle, a DEA can be modeled as a capacitor C with a varying dielectric thickness z and electrode area A. Under an actuation voltage, the thickness of a DEA decreases and its area expands, both of which increase the DEA's capacitance.The expansion of the dome under the actuation voltage is illustrated in figures 6 and 7. A multi-stacked DEA is composed of multiple layers of single-unit DEAs; therefore, the overall capacitance of a multi-stacked DEA is obtained by multiplying the number of active layers n by the capacitance of a single layer, as presented in equation (1).In this equation, ε r represents the relative permittivity of the dielectric elastomer (3.9 measured for Ecoflex ™ 00-10 mixed with the silicone thinner), and ε 0 indicates the vacuum permittivity (8.854 However, when comparing a successful vs. unsuccessful seal, we observed that the level of capacitance increase for DE suction cups was different.When the contact between the suction cup and the object's surface is successfully sealed, the fluid pressure inside the cup drops after applying the voltage; thus, the negative pressure inside the cup resists the further expansion and elevation of the dome.Subsequently, it resists a further capacitance increase.Therefore, the DEA's capacitance increases much less when the suction cup is sealed.Here, we present an analytical model and  an experimental technique to determine the success of seal formation by measuring and analyzing the capacitance value of the DE suction cups.To achieve that, we studied the relationship between the DEA's actuation voltage, deflection, and capacitance change. To model the capacitance of a DEA as a function of the input voltage, we first explain how the input voltage induces a mechanical deformation in DEAs.Equation (2), known as the Maxwell stress equation, represents the relationship between the input voltage and the transverse (i.e.cross-plane) mechanical stress built up in the dielectric elastomer, assuming that the voltage across the DEA is constant, where σ denotes the Maxwell stress, and V stands for the input voltage applied to the electrodes.
Combining this equation with the Hooks law results in: where s is the mechanical cross-plane strain due to Maxwell stress, and Y is the elastic modulus (27 kPa measured for Ecoflex ™ 00-10 mixed with the silicone thinned).We here define the stretch ratio λ, as the ratio of the elastomer thickness to the initial stressfree thickness (z 0 = 0.55 mm): We also know for the mechanical strain: Therefore: Equation ( 6) can eventually be combined with equation (3) to represent the stretch ratio of a DEA as a function of the input voltage, For the next step, we investigate how the stretch ratio affects the capacitance of DEAs, and later we derive a conclusive equation that presents the changes in capacitance directly as a function of input voltage.Overall, a reasonable approximation would be that the volume (Vol) of the dielectric elastomers remains constant while they undergo mechanical deformations because the Poisson's ratio of elastomers is very close to 0.5 [51], Therefore, it can be approximated that: where A 0 respectively represents the initial thickness of the elastomer.Accordingly, the changes in capacitance (with an initial value of C 0 ) can be rephrased as: Therefore, the change of the capacitance value of the DEAs under actuation can be formulated as the following, when the actuation voltage is applied: Finally, by combining equations ( 11) and ( 7) we achieve: Equation ( 12) represents an analytical model of a DEA's capacitance as a function of its input voltage, original layer thickness, and material parameters.This model is for a DEA with an in-plane actuation, but we approximated the model to also represent the capacitance of DE suction cups with an out-of-plane dome shape geometry.However, the mechanical resistances induced by the negative pressure of the fluid enclosed within the suction cup are not considered in this model.As mentioned before, it is expected that we would observe a significantly lower change of capacitance in DE suction cups during the gripping process when the cup is sealed to the object.
Here, we present an experimental technique to measure the DE suction cup's 'apparent capacitance' in real time.The idea is to compare the final measured capacitance with the analytical model to determine whether the suction cup has been sealed.The 'apparent capacitance' of DEAs is defined as the ratio of ACcurrent amplitude I AC to the product of AC-voltage amplitude V AC and the AC-angular frequency ω at a given actuation voltage V 0 in equations ( 13) and ( 14), The 'apparent capacitance' C app can easily be calculated from the real capacitance C as long as V AC ≪ V 0 is valid.Therefore, the current is expressed as the total change of charge Q per time in equations ( 15)-( 17), ) The apparent capacitance can now be found by combining equations ( 14) and (17), The apparent capacitance is determined by solving in equations ( 12) and ( 18) numerically.
To verify our seal detection method, we fabricated a DE suction cup with 7 active layers.The voltage and current of the DE suction cup were measured with  a sampling frequency of 500 Hz for input voltages from 1 to 6.5 kV.For each input voltage, we applied an AC voltage signal with an amplitude of 300 V and a signal frequency of 1 Hz, which corresponds to an angular frequency of 6.28 rad•s −1 , and we measured the actuator current (figure 8).Every set of measurements was performed first, when the suction cup was not in contact with the object, and the second, when the suction cup was pressed against the object under a 5 N load.To verify the repeatability of the results, each measurement was repeated five times.The capacitance measurement results for a DE suction cup with 7 active layers are shown in figure 9. Accordingly, the analytical model can predict the relative increase of the capacitance when subjected to the voltage.Moreover, the results indicate that the capacitance increase is significantly lower when the actuators are pressed against the object.This is valid, especially for voltages above 4 kV.This technique provides the DE suction cups with sensing capabilities, thereby detecting whether the suction cup has (or has not) already gripped the object before attempting to lift it.

Results and discussion
In this section, we present our studies on the negative pressures that the developed DE suction cups generated.After the suction cup contacted the object and the enclosed volume in the cup had sealed, the voltage was applied so that the enclosed fluid pressure dropped.We subsequently demonstrate the DE suction cups gripping and lifting an object, and we then discuss the results.
For characterizing the pressure and gripping performance of the suction cups, we developed a software to send the control signals to the data acquisition module (NIDAQ) (NI-9264, National Instruments).The NIDAQ sent control voltages in the range of 0-10 V to the high voltage amplifiers (HVAs) (10HVA24-P1, ULTRAVOLT) with the gain of ×1000, and received feedback voltages and currents from the monitoring units of the amplifiers.The high voltages were applied to the DE suction cup, while the actuator was lying on a 3D-printed measurement platform made of Clear Resin (Formlabs GmbH).The measurement platform was table-like in shape with a flat circular top surface.A pressure sensor (MS5839-02BA, TE Connectivity) was installed under the top surface and was connected to the top surface through a tiny hole.To avoid introducing any considerable dead volume to the suction cups, we minimized the volume of the pressure sensing line.The pressure sensor was powered by an Arduino board that was connected to a PC to log the pressure readouts.A laser sensor (scan CONTROL 3002-25/BL, Micro-Epsilon) was installed on top of the dome of the suction cups to read and record the profile of the dome.A flowchart of the measurement procedure is presented in figure 10 and the measurement setup is depicted in figure 11.
With the presented measurement method and setup, we characterized the suction behavior of the fabricated DEA.To produce the suction pressure, we applied a ramp voltage from zero to the target voltage within 2 s, and after holding the voltage for 10 s, we ramped the voltage down to zero within 2 s.We conducted the experiments for a set of actuators that had a different number of active layers (multi-stacked actuators).Figure 12(a) shows the relative pressure of the suction cup when connected to 6.5 kV for 10 s.The results indicate that there are two phases of actuation.The first step is very fast and takes place as soon as the voltage is applied.Then, the second slow phase starts.To demonstrate the gripping and lifting performance of our DE suction cups, we attached one with 7 active layers to a vertical linear stage.To test if the actuators could grasp, we 3D-printed an object with a weight of 8 g.The dimensions of the object were chosen according to the dimensions of the DE suction cup.The rim diameter of the DE suction cup was 100 mm (equal to the diameter of the substrate), which is about five times more than the diameter of the dome opening.To isolate the suction performance, we chose the cylindrical object with a diameter of 35 mm, so that the rest of the DE suction cup's rim would not influence its lifting abilities.The 3D-printed object was then put on a weight scale and placed below the suction cup, as shown in figure 13(a).We afterward lowered the linear stage with the suction cup attached to it until the suction cup contacted the object and the weight scale read 1 N, as shown in figure 13(b).Subsequently, we  applied an actuation voltage of 6 kV to enable the suction cup to grip the object.Following this, the activated suction cup was lifted meanwhile also carrying the object with it, as depicted in figure 13(c).Finally, the actuation voltage was set to 0 so that the DE suction cup would drop the object.The grip was only considered successful if the suction cup performed all of the gripping steps (approaching, grasping, lifting, and holding) flawlessly.The gripping experiment was repeated with additional weights added to the object.The DE suction cups grasped and lifted a maximum weight of 58 g with an initial contact force of 1 N.We also lifted an object with an embedded pressure sensor to learn how the pressure inside the cup changes during gripping and lifting.The results are shown in figure 14.Accordingly, from left to right, the data points called out from the graph are respectively for the actuation states: when the DE suction cup contacted the object, when the actuation voltage was applied, when the DE suction cup lifted the object from the ground, and finally, when the voltage was set to zero.
As shown in figure 14, when the suction cup was pressed against the object, the pressure inside the cup slightly increased.The actuation voltage was then applied and increased incrementally until it reached the maximum voltage within 2 s.Accordingly, the suction pressure is generated.Then, when the object was lifted, the suction cup experienced small mechanical disturbances.Finally, when the voltage was switched off, the suction pressure was quickly released.However, the pressure release was followed by a small disturbance due to the suction cup's inertia.

Discussion
There is a nuanced interplay between design and material choice when fabricating DE suction cups for soft robotics.Here we discuss the benefits and challenges that come with trying to balance the use of soft material while maintaining stability and performance.We also discuss how our DE suction cups compare to their biological counterpart.
One advantage of using DE suction cups made of elastomers with a very low elastic modulus is that they show a higher mechanical strain and deflection when compared to those composed of stiffer elastomers (equation ( 3)).In environments where a compressible fluid (like air) is the medium, larger deflections cause higher suction pressures and can therefore lift heavier objects.Furthermore, a higher deflection of the actuator causes a greater increase in the capacitance of a DE suction cup, which makes it easier to detect if the seal between the DE suction cup and the object has been formed or broken.
Another advantage of fabricating suction cups with a low elastic modulus (using the process described in this paper) is that dome recession decreases after being released from the mold.Avoiding or limiting dome recession is vital and accordingly plays a crucial role in the fabrication process.As a reminder, dome recession means that the initial height of the suction cup is less than the height of the paraboloid cavity.The important factors that cause the dome to recess are the geometry of the cavity in the mold, the thickness of the actuator, and the softness of the elastomer and the backbone.The initial height of the DE suction cup is originally determined by the geometry of the cavity inside the mold.In the fabrication process (figure 5), the planar actuator undergoes a certain amount of mechanical stress to bend and take the form of the paraboloid cavity.After depositing and curing the off-center backbone layer and removing the actuator from the mold, the built-up stress in the actuator counteracts the non-planar form, which results in a dome recession.Actuators with more active layers (i.e.thicker) show more significant recession because stiffer elastomers require more elastic energy to assume the geometry of a suction cup; therefore, the counteracting flattening stresses are stronger for stiffer and thicker DE suction cups.This becomes more evident as we compare the dome recession of actuators with 2 vs. 5 active layers, as illustrated in figure 15.Accordingly, the suction cup with 5 active layers is thicker, thus it has less initial height.To structurally support the pre-formed dome, we can deposit backbone layers that have a higher elastic modulus or higher thickness.
However, if the actuator is too soft and thin it loses its dome shape due to gravity alone.This can be observed in the profile of the suction cup with 1 active layer (figure 15).A solution to avoid such deformations would be to optimize the geometry of the cavity regarding the geometry and mechanical properties of the actuator.That is because the geometry of the cavity influences the stability of the dome structure.Paraboloids with wider openings and smaller heights are less stable (especially for thinner actuators) because the center of the dome receives less mechanical support from the rim and carries a higher share of the dome's weight.It can be compared to having a wide ceiling area without any support pillars in the middle to hold the ceiling's weight.
Similar to the discussion on the deflection and deformation of the actuators, the softness of the dome as well as the geometry of the paraboloid cavity also affect the suction pressure.Soft and thin actuators lose their form when the enclosed pressure drops more than a certain value, as illustrated in figure 16.The dome deforms mainly because its structure is not stable enough to withstand the weight of its dome due to gravity alone, and also due to the suction pressure of the enclosed air which pulls the dome inwards.At higher actuation voltages, the dome gets thinner due to Maxwell stress, and the difference between the ambient pressure and the air pressure inside the suction cup increases.Both of these increase the instability of the dome structure.Therefore, the dome structure deforms mostly at higher actuation voltages, especially for thinner actuators (those with a lower number of active layers).Increasing the number of active layers, thereby enhancing the overall thickness of the dome, results in a stiffer and more stable structure.This modification effectively delays the onset of the critical voltage threshold at which the dome loses its characteristic shape.When deformation due to instability occurs, higher actuation voltages do not increase the volume of the DE suction cup and do not generate more suction pressures.This effect can be observed in figure 12(b), which presents a comparison of the suction pressure of actuators with different numbers of layers.We can see that the pressure drop at 6.5 kV does not follow the same trend as the pressure decreases until 6 kV.We can also see that the kink at 6.5 kV is more pronounced for thinner actuators and with a lower number of active layers.Ultimately, said kink is virtually negligible for the suction cup with 7 active layers.In this case, larger actuation voltages still cause more negative pressures, allowing the DE suction cup to lift heavier objects.Nevertheless, we did not apply voltages of more than 6.5 kV for characterizing the suction pressure or more than 6.0 kV for testing the lift.That is because we observed a breakdown voltage of around 7 kV for the DE suction cups.
Recognizing the limitations of our breakdown voltage, it is crucial to further examine how our design compares to its biological role model.Octopus suckers have a very complex system made of different muscles.Furthermore, the mucus discharged by the octopus sucker significantly improves the seal between the object and the suction cup.In contrast, DE suction cups only use one artificial muscle to apply the suction pressure.Additionally, the absence of mucus and radial muscles makes sealing and detaching more difficult for DE suction cups.From a performance point of view, the octopus sucker can generate a suction pressure of about 65 kPa at sea level [28], while our DE suction cups can maximally generate a suction pressure of 1.3 kPa, which is considerably less.The differences between biological and DE suction cups leave room for improving the design and fabrication of DE suction cups.

Conclusion and outlook
To conclude, in this paper, we presented the design and fabrication of DE suction cups inspired by the suction mechanism of octopus suction cups.We explained the suction mechanism of suction cups and pointed out how DE suction cups can mimic this mechanism.We elaborated on the fabrication steps of multi-stacked DEAs.Within this, we presented our novel design and fabrication technique that stabilizes the dome shape by spin-coating and curing a backbone silicone layer off-center onto the pre-domed actuator.The developed actuators are fully soft, do not have embedded rigid parts, and do not require any external rigid frame to be pre-stretched over.They are able to function only with high voltages and do not require any external support to hold the dome shape and function.The fabrication process (including the materials and devices) is inexpensive, straightforward, relatively fast, and reproducible.
Following that, we introduced the measurement setup and the characterization methods; then we presented and discussed the characterization results.We measured the suction pressure of the enclosed air in the suction cups.The suction cups with 7 active layers generated a maximum negative pressure of 1.3 kPa under an actuation voltage of 6.5 kV.We finally presented the setup for performing lift tests.The suction cup with 7 active layers successfully lifted an object with 58 g under an actuation voltage of 6 kV.
Future work will characterize the set of suction cups under different circumstances, such as actuating underwater.In this study, we applied actuation voltages as high as 6.5 kV to the DE suction cups, which could be dangerous to humans.Passive silicone layers covering the electrodes provide a level of security, but insulation should and will also be extended to cover the connecting wires which would also be an important step for actuating the DE suction cups underwater.Furthermore, in regards to DE suction cups underwater, we will also consider fabricating actuators with higher elastic modulus.This is because DE suction cups do not need to deflect significantly to generate suction pressures underwater, due to the incompressibility of the medium.However, instability and deformation of the dome could occur at high voltages.
Another future work will be to decrease the dimension of the suction cup's rim and optimize the cavity dimensions in the mold to minimize dome recession.The rim of the DE suction cup can be scaled down by choosing a smaller substrate for the spincoating machine from the beginning or even cutting the rim after fabricating the DE suction cup.Additionally, different dimensions and geometrical shapes of the cavity will be studied to avoid deforming the dome at high voltages.This approach aims to achieve more deflections or suction pressures, depending on the application.In this work, we selected one of the softest commercially available silicones and fabricated DE suction cups with a similar elastomer thickness for each active layer.In the future, we will fabricate and characterize new sets of DE suction cups with different elastomeric materials to compare their actuation behavior.In addition, we will fabricate DE suction cups with thinner elastomer layers to decrease the actuation voltage.These studies rely on mathematical or simulation models that predict the deflection and suction pressure of the actuators according to their geometrical and physical properties.As such, we plan to develop the required accurate predictive model in the future.
Last but not least, in this article, we have demonstrated the ability of the artificial suction cup to lift a 3D-printed object with a flat surface.Theoretically, our method could work for lifting curved surfaces as well, as this only requires that DE suction cups are compliant.Since our fabrication method has no rigid parts, the fully soft DE suction cups are compliant and, therefore have the potential to seal to curved surfaces.However, we only used objects with flat surfaces for the lift test; therefore, we do not have any data on lifting objects with curved surfaces, such as eggs.In the future, we will study how the curvature of an object's surface affects the lifting performance of the DE suction cups.

Figure 1 .
Figure 1.Morphology and suction mechanism of octopus tentacles; (a) a drawing of the morphology of an octopus suction cup where A is the acetabulum, I is the infundibulum, and C, R, and M represent the circular, radial, and meridional muscles, respectively [28], and (b) surface and volume increase of acetabulum due to contraction of radial muscles which results in a pressure drop of the enclosed fluid.Adapted with permission from [28].

Figure 2 .
Figure 2. Actuation mechanism of a DEA.The Maxwell stress caused by the actuation voltage compresses the dielectric in thickness and expands its area.

Figure 3 .
Figure 3. Fabrication steps of flat and planar DEAs with one active layer; (a) applying the passive elastomer on the substrate and spinning, (b) depositing the passive elastomer layer evenly and curing it at 80 • C, (c) painting CB powder onto the elastomer layer with a soft brush using a patterned negative mask (depicted in blue), (d) applying an elastomer compound and spinning, (e) curing the deposited active elastomer layer at 80 • C, (f) painting the second electrode layer similar to step '(c)' , (g) applying the third elastomer layer and spinning, (h) curing the actuator at 80 • C, and (i) the cross-section of the actuator.To produce actuators with multiple active layers, steps '(c)' , '(d)' , and '(e)' are repeated.

Figure 4 .
Figure 4. Fabrication steps of the suction cup using a negative mold and the photographs of the resulting suction cups; (a) a 3D-printed negative mold with a paraboloid cavity, (b) placing the flat DEA on the mold and the paraboloid cavity, (c) applying and spinning the uncured backbone material onto the actuator offset from the center of the cavity, (d) applying soft silicone elastomer compound offset from the center of the cavity, directly on the cured backbone layer, (e) curing the soft silicone layer, and (f) removing the mold and flipping the suction cup.

Figure 5 .
Figure 5. Fabricated suction cup; (a) backside view of the suction cup after curing the Smooth-Sil ™ 950 backbone, and (b) side-view of the suction cup with the focus on the actuator's dome.

Figure 6 .
Figure 6.Deflection of a suction cup with 5 active layers when the cup is not in contact with an object; (a) initial form of the dome under 0 kV, and (b) the deflected dome under 6.5 kV.

Figure 7 .
Figure 7. Profile of the unsealed suction cup with and without actuation, captured with a laser profilometer.

Figure 8 .
Figure 8. Voltage and current of a DE suction cup with 7 active layers when an AC voltage signal with amplitude of 300 V is applied on top of 5 kV DC actuation voltage.

Figure 9 .
Figure 9. Relative capacitance-change for a DE suction cup when it is pressed against an object (sealed) compared to when it is not in contact with the object (not sealed).The base capacitance Co in this experiment was 240 pF for the DE suction cup with 7 active layers.

Figure 11 .
Figure 11.Measurement setup for characterizing the suction cups.

Figure 12 .
Figure 12.Pressure of the enclosed air within suction cups; (a) pressure-drop of the actuator with 5 active layers over time for 14 s of actuation (2 s ramp up, 10 s constant, then 2 s ramp down), and (b) the maximum pressure-drop per voltage for actuators with a different number of layers.

Figure 13 .
Figure 13.Gripping setup for lifting objects; (a) approaching, (b) contacting with a 1 N initial force and activation under 6 kV, and (c) lifting and holding a 58 g object.

Figure 14 .
Figure 14.Air pressure change in the suction cup during the lifting and releasing of an object.From left to right, the given numbers in the bracket respectively specify the time and the pressure when the suction cup contacted the surface, when the voltage was applied, when the object was lifted, and when the actuation voltage was set to zero.

Figure 15 .
Figure 15.Profile of the suction cup under zero voltage for actuators with 1, 2, and 5 active layers.

Figure 16 .
Figure 16.Thin suction cup with 1 active layer losing its dome structure under 6.5 kV due to the suction pressure.

Table 1 .
Fabrication recipe of soft dielectric elastomer suction cups.
[57]cause Ecoflex ™ 00-30 has a low viscosity, it is easier to deposit very thin passive layers with the spin-coating technique[57].